This invention relates generally to a computer method and apparatus for constructing graphs mathematically and aesthetically representing graphs as graphics, and more particularly to a computer method and apparatus for constructing graphs using a graph algebra and then visually or otherwise representing the graphs as a quantitative aesthetic graphic representation.
Until recently, graphics were typically drawn by hand to represent mathematical, statistical, and geometric relations. Computer graphics programs, particularly scientific and mathematical plotting packages, have made this task much easier but they have not altered its ad hoc aspect. Nor have statistical and mathematical packages that generate more complex graphics contributed to our understanding of how they are created.
A need exists for a computer method and system to be able to construct graphics systematically in order to handle more complex multivariate environments. This is also the case in connection with data mining computer systems. Unfortunately, the sophistication of data mining systems far exceeds the computer graphical methods used in their displays. Most data mining computer systems still rely on pie, line, and bar charts of slices of data cubes (multi-way aggregations of a subset of a database). These charts fail to reveal the relationships among the entities they represent because they have no deep grammar for generating them. They are simply hard-wired to facets of the data cube. For example, if one drills through the cube to view a different slice of the data, only a simple pie chart is obtained. A similar hard-wiring exists in displays from tree classifiers, neural networks, and other algorithms.
A need also exists for a method and apparatus for creating aesthetic graphics from data using graph algebra.
In accordance with the present invention, a computer method is provided for creating quantitative graphics using graph algebra.
In accordance with another aspect of the present invention, a data processing system is provided for constructing graphs mathematically using a graph algebra and displaying the graphs aesthetically as graphics, which can be a visual or other sensory display of the underlying mathematical graph.
In accordance with still another aspect of the present invention, a non-volatile storage medium is provided containing computer software encoded in a machine readable form for creating graphs mathematically using a graph algebra and for displaying the mathematical graph aesthetically, such as a visual representation.
In accordance with the invention, a method for creating quantitative graphics includes performing the following steps on a computer: indexing data to form a data set; converting the data set into a variable data structure, where the variable data structure is an index set; converting the variable data structure into a variable set by using at least one operation selected from the group consisting of a blend operator, a cross operator, and a nest operator; mapping the variable set into a set of points; and mapping the set of points into an aesthetic representation, which may be a visual graphic.
In accordance with another aspect of the present invention, a method is provided for creating quantitative graphics that includes the steps of: providing a list of variables; providing a list of representations for points; providing a list of coordinate systems; providing a list of aesthetic representations; selecting at least one variable from a list of variables; selecting at least one representation for points from the list of representations for points; selecting at least one coordinate system from the list of coordinate systems; selecting at least one aesthetic representation from the list of aesthetic representations; moving the at least one variable to a predetermined location; and displaying a visible graphic reflecting the at least one variable, the at least one representation for points, the at least one coordinate system and the at least one aesthetic representation.
In accordance with another aspect of the invention, the data processing system for constructing graphs mathematically and aesthetically representing the graphs as graphics includes: a computer processor; and a memory responsively coupled to the computer processor containing a set of computer instructions for: (a) indexing data to form a data set; (b) converting the data set into a variable data structure, where the variable data structure has an index set, a range and a function; (c) converting the variable data structure into a variable set by using at least one operator selected from the group consisting of a blend operator, a cross operator, and a nest operator; (d) mapping the variable set into a set of mathematical points; and (e) mapping the set of mathematical points into an aesthetic representation.
In accordance with still another aspect of the present invention, a non-volatile storage medium containing computer software encoded in a machine readable format for creating quantitative graphics is provided. The non-volatile storage medium includes: a set of computer instructions for indexing data to form a data set; a set of computer instructions for converting the data set into a variable data structure, where the variable data structure has an index set, a range and a function; a set of computer instructions for converting the variable data structure into a variable set by using at least one operator selected from the group consisting of a blend operator, a cross operator, and a nest operator; a set of computer instructions for mapping the variable set into a set of points; and a set of computer instructions for mapping the set of points into an aesthetic representation.
The methods, systems and devices in accordance with the invention allow data to be manipulated in many different ways and also represented by graphics in many different ways. Thus, the creation of graphics in accordance with the present invention is not limited by the constraints of graphical representations that are mere aggregations of a subset of a database.